Let $X$ be an arbitrary topological space, let $Y$ be an ordered set in the order topology, and let the maps $f, g \colon X \to Y$ be continuous. Then how to show that the set $S$ given by $$S \colon= \{ \ x \in X \ \colon f(x) \leq g(x) \ \}$$ is closed in $X$?
2026-04-01 00:25:32.1775003132
Problem 8 (a) in Exercises after Sec. 18 in Munkres' Topology, 2nd ed.: How to show this set is closed?
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